9. Probability computations using the standard normal distribution Aa Assume tha

Question

9. Probability computations using the standard normal distribution Aa Assume that X, the starting salary offer for psychology majors, is normally distributed with a mean of $47,507 and a standard deviation of $5,000. Use the following Distributions tool to help you answer the questions. (Note: To begin, click on the button in the lower left hand corner of the tool that displays the distribution and a single orange line.) Standard Normal Distribution Mean = 0.0 Standard Deviation = 1.0 .5000 5000 -4 0.0000 The probability that a randomly selected psychology major received a starting salary offer greater than $52,000 is

Explanation / Answer

Ans:

Mean=47507

standard deviation=5000

z=(x-mean)/standard deviation

When x=52000

z=(52000-47507)/5000=0.8986

P(z>0.8986)=1-P(z<=0.8986)

=1-0.8156

=0.1844

when x=45000

z=(45000-47507)/5000=-0.5014

P(-0.5014<=z<=0.8986)=P(z<=0.8986)-P(z<=-0.5014)

=0.8156-0.3080

=0.5076

z score when x=38000

z=(38000-47507)/5000=-1.90

P(-1.90<=z<=-0.5014)=P(z<=-0.5014)-P(z<=-1.9)=0.3080-0.0287=0.2793

Correct option is 27.98%

P(Z<=z)=0.2

z=-0.8416

x=47507-0.8416*5000

x=43299

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